Calculate the value of E.A.N of metal cation in `[Cu(NH_(3))_(4)]SO_(4)` complex

Explanation

To calculate the Effective Atomic Number (E.A.N) of the metal cation in the complex \([Cu(NH_3)_4]SO_4\), we will follow these steps:

### Step 1: Identify the oxidation state of the metal cation (Cu).
The complex \([Cu(NH_3)_4]SO_4\) consists of a copper ion coordinated with four ammonia ligands and a sulfate ion as the counter ion. Ammonia (NH₃) is a neutral ligand, so it does not contribute to the charge. The sulfate ion (SO₄²⁻) has a charge of -2.

Since the overall charge of the complex must balance with the sulfate ion, the oxidation state of copper must be +2.

### Step 2: Determine the atomic number of the metal cation (Cu).
The atomic number of copper (Cu) is 29.

### Step 3: Calculate the total electron count contributed by the ligands.
Each ammonia (NH₃) ligand donates 2 electrons to the metal center. Since there are 4 ammonia ligands, the total electron contribution from the ligands is:
\[ 4 \text{ (NH}_3\text{)} \times 2 \text{ electrons} = 8 \text{ electrons} \]

### Step 4: Calculate the Effective Atomic Number (E.A.N).
The formula for E.A.N is given by:
\[ \text{E.A.N} = \text{Atomic number of metal} + \text{Total electron count from ligands} - \text{Oxidation state of metal} \]
Substituting the values we have:
- Atomic number of Cu = 29
- Total electron count from ligands = 8
- Oxidation state of Cu = +2

Now, substituting these values into the formula:
\[ \text{E.A.N} = 29 + 8 - 2 = 35 \]

### Final Answer:
The Effective Atomic Number (E.A.N) of the metal cation in the complex \([Cu(NH_3)_4]SO_4\) is **35**.

---